Friday, March 22, 2013

The Economics of 50/50 Draws

"Boy," you might be saying, "this blog has sure posted a lot this month!" You're right! In fact, March so far has had at least twice as many page views as any other month in the existence of this blog. Figuring that this is about as successful as this is ever going to get, I figured I'll just keep posting while the going is hot.

Recently I attended a fair number of arena curling games. People who attend arena curling games often enjoy things like expensive beer, ridiculously addictive popcorn, curling (sometimes), and the 50/50 draw.

A fun way to think about casino games and lotteries (if you're me) is based on their expected return (ok, it's actually not fun at all).

Take Roulette, for instance. If you pick a solid colour in Roulette you have an 18/38 chance of winning, where winning would double your money. Doubling your money isn't quite good enough to break even, though, because 18/38 is slightly less than half. As a result, for every dollar you spend on Roulette, you'd expect to lose 5.26 cents. This is the house edge for Roulette, and what ensures that the casino always comes out on top.

Other common casino games have house edges like 1.41% (pass line in craps), 1.06% (banker bet in Baccarat), and 0.43% (perfect play in Blackjack without counting cards). Slot machines will often run house edges ranging from 7%-15%.

Lotteries are a little bit different. Lotto 6/49, for instance, runs a house edge of about 30%, Keno gambling is approximately 30%-40% depending on the rules, and I suspect that sports betting using SportSelect can get as high as 30%-50%.

Now that we have a reference point, we can compare 50/50 lotteries to these other games. In a basic 50/50 game, everyone could buy $5 tickets, and one person would win 50% of all the money paid into the lottery. Buying one ticket would give you a 1/n chance of winning, and you would win an amount of money equivalent to n/2 time the price per ticket, at a cost of entry of that same price per ticket. As a result, your expected loss per ticket purchased is 50%. This is way worse than pretty much anything else.

Things get a little bit more complicated though. Many arenas nowadays offer the option of paying $5 for 1 ticket, $10 for 3 tickets, or $20 for 10 tickets. Apart from the obvious differences in price per ticket (making $20 for 10 seem a substantially better deal already), how do these different options translate into house edges?

Fortunately I made another set obscure and hard-to-read ternary plots for ya! Check it out:

Due to me not thinking before colouring, the axes are a bit backwards. Along the bottom is the fraction of sales for the $5/1 combo, along the right hand side is the fraction of sales for the $10/3 combo, and along the left hand side is the fraction of sales for the $20/10 combo. If you've never read one of these, check out this cool website on how to do so.

In general, the house edge depends on what everyone else buys, which makes sense. It's interesting just how large this effect is, though. Buying a single ticket for $5 ranges from a house edge of 50% (if everyone else does too) to 80% (if everyone else buys the best combo).

Buying three tickets for $10 ranges from a house edge of 25%-70%, and buying ten tickets for $20 ranges from a house edge of 50% to a player edge of 25%. The player edge, of course, only occurs if you are one of a very tiny number of people buying the $20/10 combo.

Though I can't find any sources for the actual distribution at sporting events, if we had an even split in sales then we'd be looking at a house edge ranging from 40%-75%, depending on which package is purchased. This is by far the worst set of house odds out of any of the games previously mentioned.

50/50 draws are maybe justified in the sense that the money primarily goes to charities, but as an investment (or even just a source of gambling for fun) they're really probably one of the worst things you can do.

See ya!

7 comments:

Anonymous said...

Thank you so much, Mike, for taking the time to post this valuable information on 50/50 draws. You just saved me a bunch of money !

Richard said...

The statistics will be better if people started to learn how to play https://casinority.com/15-winning-roulette-strategies/ Because everyone want to win big without any effort except driving to Las Vegas

Alma N. Lassen said...

Maximum programmer are sometime offer programming homework for money. But you will not take your homework from any programmer. You try to understand which is best.

Anonymous said...

This is great I am sure that such useful things should appear on great resources like realcuriousworld.

George Ewumbua said...

It is a very hard situation when playing the lottery and never won, or keep winning low fund not up to 500 bucks, i have been a victim of such a tough life, the biggest fund i have ever won was 350 buck, and i have been playing the lottery for almost 8 years now, things suddenly change the moment i came across a secret online, a testimony of a voodoo doctor who help people in any type of lottery numbers, i was not easily convinced, but i decided to take try, now i am a proud lottery winner with the help of Dr Aziba, i won $5.000.0000.00 and i am making this known to every one of you who have been trying all day to win the lottery, believe me this is the only way to win the lottery, this is the real secret we all have been searching for, you can contact Dr Aziba on his Email>priestazibasolutioncenter@gmail.com Website: http://priestazibasolutioncenter.webs.com
good luck.

Clare said...

I am so overwhelmed and grateful to you and the magic you have done that make me win millions of dollars in lottery. I would like to say,-Thank you. I was on the edge of losing my house and so many things around me, so I asked a spell from you, so that I will be able to save my house and come up with payment options. He help me with his magic spell and i win 70,000.00 $ all thinks goes to dr. Aziba for what him has just done for me. Sure enough,-what I asked for. You have proven over and over again, that you are the best spell caster. any body out there that is reading this my testimony,you have to hurry and get in touch with the spell cast,so that he can help you to win the lottery. Email: Priestazibasolutioncenter@gmail.com
Website: http://priestazibasolutioncenter.webs.com
WhatApp: +2348100368288

LISA ALICE said...

I use to be a very poor woman who has always not find luck when it comes to playing the lottery. I have been playing lottery since i was 21 years and now i am 45 meaning i have been playing lottery for 24 years. The biggest amount i have ever won in my life was 400 bucks. But one day my story turns to history after i find this man name on the Internet that he is the best when it comes to winning lottery. This man is a very strong voodoo doc who gives out the numbers that can never fail. After all my years of laboring and struggling to win the lottery i finally won ( $62,000,000) Dr Alli is the name, email is allispellhelp1@gmail.com or allispellhelp@yahoo.com
+2348100772528 this is the only way to win the lottery and the best way.